#LnormInf corresponds to the absolute value of the greatest element of the vector. X = x*(1-omega) + (omega/A)*(b - np.dot(A, x) - np.dot(A, x_old)) In numerical linear algebra, the GaussSeidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method. Print ('The solution vector in iteration', iter1, 'is:', x)

I know that the spectral radius is the maximum eigenvalue however I am still confused by the question. The Poisson Equation in Any Space Dimensions def sor_method(A, b, omega, initial_guess, tolerance, max_iterations): a)I need to find the spectral radius of the Jacobi and Gauss-Seidel iteration matrices from the given matrix. See section 3 on the paper The Optimal Relaxation Parameter for the SOR Method Applied to I am supposed to make a function that uses Gauss-Jacobi method to solve an augmented matrix but cant figure out why my solution is always 0,0,0. Obviously, with higher omega values the number of iterations should decrease.Īs for a working algorithm on SOR this is what I have computed, where best convergence is reached when the optimal omega is used. Phi = sor_solver(A, b, omega, initial_guess, residual_convergence)įor an extended answer on omega and its uses please refer to my other answer SOR method as what is quoted below is not accurate. #An example case that mirrors the one in the Wikipedia article Here I have some python script, which solves the system of linear equations using Gauss-Seidel method: import numpy as np

Gauss seidell method in python